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UMI

UMI. Wednesday July 9. Welcome! Min. Good Morning! Announcements or Questions. Overview of the Day. Place value Addition and subtraction Logical reasoning Multiple representations Procedural fluency Algebraic Patterns.

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  1. UMI Wednesday July 9

  2. Welcome! Min Good Morning! Announcements or Questions

  3. Overview of the Day • Place value • Addition and subtraction • Logical reasoning • Multiple representations • Procedural fluency • Algebraic Patterns

  4. Warm Up Min • Use a traditional clock face to determine the next three terms in the following sequence: 1, 9, 5, 1 … 2. 3. What are the three ways to solve ? 4. Write 7 hundred thousand seven in both standard and expanded form. 5. There are 4 girls and 10 boys at the show. Is the ratio of girls to boys 2:5 or 5:2?

  5. Place Value ah ROUNDING

  6. Place Value • When the distance to the moon is given as 240,000 miles, the number represents an approximation to the true distance. • Giving an approximate value for an exact number is called rounding. • A number is always rounded to a given place value.

  7. Place Value

  8. Place Value

  9. Place Value • A whole number is rounded to a given place value without using the number line by looking at the first digit to the right of the given place value. • If the digit to the right of the given place value is less than 5, that digit and the digits to the right are replaced by zeroes.

  10. Place Value ah • Let’s round 13,834 to the nearest hundred. 13, 834 • 13,834 rounded to the nearest hundred is 13,800. Given place value 3 < 5

  11. Place Value • If the digit to the right of the given place value is greater than or equal to 5, increase the digit in the given place value by 1, and replace all other digits to the right by zero. • Let’s try an example--

  12. Place Value • Try these examples— • Example 1 Round 525, 453 to the nearest ten- thousand. • 530,000 • Example 2 Round 1972 to the nearest hundred. • 2000

  13. Place Value • Example 3 Round 368, 492 to the nearest ten- thousand. • 370,000 • Example 4 Round 3962 to the nearest hundred. • 4000

  14. Place Value EXTENDING THE PLACE VALUE SYSTEM • Important idea 1 • The grouping idea should be generalized. • That is, 10 in any position makes a single thing (group) in the next position, and vice versa.

  15. Place Value EXTENDING THE PLACE VALUE SYSTEM • Important idea 2 • The oral and written patterns for numbers in three digits are duplicated in a clever way for every three digits to the left.

  16. Place Value • Reflection • How would you describe good place value number sense? There are a variety of aspects to number sense with large numbers. Describe activities that are designed to help develop these different features of good number sense with larger numbers.

  17. Place Value • Virtual Manipulativeshttp://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/common/itools_int_9780547584997_/numbercharts.html • http://www.eduplace.com/kids/hmcam/swfs/manip/tablesh1/tablesh1.html • http://www.k6.thinkcentral.com/content/hsp/math/hspmath/na/common/itools_int_9780547584997_/basetenblocks.html

  18. Logical Reasoningah • At a recent painting competition, Eileen’s rendition of A Constable was not last. Jenny only just managed to avoid last place and came third. The lady who painted a Monet was very successful and took first place. Ada beat the lady who painted the Taylor and the lady who painted the Van Gogh beat Vera. Can you determine who painted what and who won?

  19. Multiple Representationskac • Using Screen Shots for Multiple Representations

  20. Procedural Fluency ah • In order to be really fluent, students must understand the mathematics of the facts they are expected to memorize. • Fluency comes at the endpoint of clear learning progressions as documented in the core standards. • Students should experience the use of concrete and pictorial representations of math problems.

  21. Procedural Fluency ah • https://www.youtube.com/watch?v=ZFUAV00bTwA

  22. Transition kac • Stand • Do 3 jumping jacks or turn around 3 times • Touch your toes or knees…whichever you like • Say hi to someone across the room • Find your chair and we will begin, again!

  23. Addition and Subtraction kac • Natural, whole, integers, rational, irrational • Properties • Closure • If you add two numbers the answer must be from the set of numbers you are using. • (2 + 3 = 5) • .

  24. Addition and Subtraction • Commutative • (4 + 6) = (6 + 4) • Associative • (2 + 3)+ 9 = (9 + 3) +2 • Identity • 4 + 0= 4 • Do they work for both + and -?

  25. Addition • Counting on • Doubles • Making ten • Counting back

  26. Addition…new to you? • Left to right algorithm • Lattice Algorithm • + 7 1 1 6

  27. Let’s practice • 476 + 229

  28. Subtraction • Take away • Missing addend • Comparison • Number line

  29. Subtraction…new to you? • Equal Additions Algorithm 255 255 +7 262 262 +30 292 -163 -163 +7 -170 -170 + 30 -200 • Expanded form -243 61

  30. Let’s Practice • Equal Addition Algorithm 293-177 • Expanded Form 399-177

  31. Algebraic Patterns md • Patterns are everywhere in the world! • Finding and understanding patterns would enable us to foresee the future. • With patterns we could discover new things and better understand the world around us.

  32. Algebraic Patterns • Patterns Match – Colors • Patterns Match – Shapes • Pattern Match - Numbers

  33. Algebraic Patterns Number Patterns • Arithmetic Sequences Example: 1, 5, 9, 13, 17,21,25,… This sequence has a difference of 4 between each number. The pattern is continued by adding 4 to the last number each time, like this:

  34. Algebraic Patterns • The value added each time is called the "common difference"

  35. Algebraic Patterns Example: 18, 15, 12, 9, 6, 3,… This sequence has a common difference -3.The pattern is continued by subtracting 3 to the last number each time, like this:

  36. Algebraic Patterns Geometric Sequences Example : 1, 2, 4, 8, 16, 32,… This sequence has a factor of 2 between each number.The pattern is continued by multiplying by 2 each time, like this:

  37. Algebraic Patterns • The value multiplied each time is called the "common ratio"

  38. Algebraic Patterns Example: 18, 6, 2, 2/3, 2/9, 2/27,… This sequence has a common ratio 1/3.The pattern is continued by multiplying 1/3 to the last number each time, like this:

  39. Algebraic Patterns Function Machine From algebraic patterns to functions (rules) Function is like a machine that has an input and an output. Therefore a function has three parts, • Input • Output • Rules Input and output are related by rules.

  40. Algebraic Patterns • Function machine for grade 3-4 • Function machine for grade 5-6

  41. Closure ah • Today one topic we worked on was Algebraic Patterns. Think to yourself what you already incorporate into your math curriculum and what changes you might make in your curriculum after today’s work. • In your notebook, write the main ideas you learned and how you might easily incorporate these ideas in your math class. • Share your ideas with the entire class.

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